Fangzhen Lin

Golog: A logic programming language for dynamic domains

Abstract This paper proposes a new logic programming language called GOLOG whose interpreter automatically maintains an explicit representation of the dynamic world being modeled, on the basis of user supplied axioms about the preconditions and effects of actions and the initial state of the world. This allows programs to reason about the state of the world and consider the effects of various possible courses of action before committing to a particular behavior. The net effect is that programs may be written at a much higher level of abstraction than is usually possible. The language appears well suited for applications in high level control of robots and industrial processes, intelligent software agents, discrete event simulation, etc. It is based on a formal theory of action specified in an extended version of the situation calculus. A prototype implementation in Prolog has been developed.

ASSAT: computing answer sets of a logic program by SAT solvers

We propose a new translation from normal logic programs with constraints under the answer set semantics to propositional logic. Given a logic program, we show that by adding, for each loop in the program, a corresponding loop formula to the programs completion, we obtain a one-to-one correspondence between the answer sets of the program and the models of the resulting propositional theory. Compared with the translation by Ben-Eliyahu and Dechter, ours has the advantage that it does not use any extra variables, and is considerably simpler, thus easier to understand. However, in the worst case, it requires computing exponential number of loop formulas. To address this problem, we propose an approach that adds loop formulas a few at a time, selectively. Based on these results, we implemented a system called ASSAT(X), depending on the SAT solver X used, and tested it on a variety of benchmarks including the graph coloring, the blocks world planning, and Hamiltonian Circuit domains. The results are compared with those by smodels and dlv, and it shows a clear edge of ASSAT(X) over them in these domains.

How to progress a database

Abstract One way to think about a STRIPS operator is as a mapping from databases to databases, in the following sense: suppose we want to know what the world would be like if an action, represented by the STRIPS operator α, were done in some world, represented by the STRIPS database D 0. To find out, simply perform the operator α on D 0 (by applying αs elementary add and delete revision operators to D 0). We describe this process as progressing the database D 0 in response to the action α. In this paper, we consider the general problem of progressing an initial database in response to a given sequence of actions. We appeal to the situation calculus and an axiomatization of actions which addresses the frame problem (Reiter (1991)). This setting is considerably more general than STRIPS. Our results concerning progression are mixed. The (surprising) bad news is that, in general, to characterize a progressed database we must appeal to second-order logic. The good news is that there are many useful special cases for which we can compute the progressed database in first-order logic; not only that, we can do so efficiently. Finally, we relate these results about progression to STRIPS-like systems by providing a semantics for such systems in terms of a purely declarative situation calculus axiomatization for actions and their effects. On our view, STRIPS operators provide a mechanism for computing the progression of an initial situation calculus database under the effects of an action. We illustrate this idea by describing two different STRIPS mechanisms, and proving their correctness with respect to their situation calculus specifications.

On strongest neccessary and weakest sufficient conditions

Abstract Given a propositional theory T and a proposition q , a sufficient condition of q is one that will make q true under T , and a necessary condition of q is one that has to be true for q to be true under T . In this paper, we propose a notion of strongest necessary and weakest sufficient conditions. Intuitively, the strongest necessary condition of a proposition is the most general consequence that we can deduce from the proposition under the given theory, and the weakest sufficient condition is the most general abduction that we can make from the proposition under the given theory. We show that these two conditions are dual ones, and can be naturally extended to arbitrary formulas. We investigate some computational properties of these two conditions and discuss some of their potential applications.

Ability and knowing how in the situation calculus

Most agents can acquire information about their environments as they operate. A good plan for such an agent is one that not only achieves the goal, but is also executable, i.e., ensures that the agent has enough information at every step to know what to do next. In this paper, we present a formal account of what it means for an agent to know how to execute a plan and to be able to achieve a goal. Such a theory is a prerequisite for producing specifications of planners for agents that can acquire information at run time. It is also essential to account for cooperation among agents. Our account is more general than previous proposals, correctly handles programs containing loops, and incorporates a solution to the frame problem. It can also be used to prove programs containing sensing actions correct.

A logic of knowledge and justified assumptions

Abstract In this paper we define the logic GK of knowledge and justified assumptions. GK is best understood as a formalization of autoepistemic reasoning processes that are more general than those in Moores autoepistemic logic, and is formally defined via a modification of Shohams preference semantics. We show that GK includes not only Moores autoepistemic logic, but also Reiters default logic. To our knowledge GK is the first complete semantic unification of the two logics. Similarly to circumscription, GK is based on the notion of logical minimization, and thus provides a bridge between circumscription and fixed-point nonmonotonic logics, an outstanding problem in nonmonotonic logics. As an application of this bridge, we propose a formalization of logic programs with negation-as-failure in circumscription.

Computer-aided proofs of Arrow's and other impossibility theorems

Arrows Impossibility Theorem is one of the landmark results in social choice theory. Over the years since the theorem was proved in 1950, quite a few alternative proofs have been put forward. In this paper, we propose yet another alternative proof of the theorem. The basic idea is to use induction to reduce the theorem to the base case with 3 alternatives and 2 agents and then use computers to verify the base case. This turns out to be an effective approach for proving other impossibility theorems such as Sens and Muller-Satterthwaites theorems as well. Furthermore, we believe this new proof opens an exciting prospect of using computers to discover similar impossibility or even possibility results.

Alternating Fixpoint Theory for Logic Programs with Priority

van Gelders alternating fixpoint theory has proven to be a very useful tool for unifying and characterizing various semantics for logic programs without priority. In this paper we propose an extension of van Gelders alternating fixpoint theory and show that it can be used as a general semantic framework for logic programs with priority. Specifically, we define three declarative and model-theoretic semantics in this framework for prioritied logic programs: prioritized answer sets, prioritized regular extensions and prioritized well-founded model. We show that all of these semantics are natural generalizations of the corresponding semantics for logic programs without priority. We also show that these semantics have some other desirable properties. In particular, they can handle conflicts caused indirectly by the priorities.

Abduction in logic programming: a new definition and an abductive procedure based on rewriting

A long outstanding problem for abduction in logic programming has been on how minimality might be defined. Without minimality, an abductive procedure is often required to generate exponentially many subsumed explanations for a given observation. In this paper, we propose a new definition of abduction in logic programming where the set of minimal explanations can be viewed as a succinct representation of the set of all explanations. We then propose an abductive procedure where the problem of generating explanations is formalized as rewriting with confluent and terminating rewrite systems. We show that these rewrite systems are sound and complete under the partial stable model semantics, and sound and complete under the answer set semantics when the underlying program is so-called odd-loop free. We discuss an application of abduction in logic programming to a problem in reasoning about actions and provide some experimental results.

From answer set logic programming to circumscription via logic of GK

We first provide a mapping from Pearces equilibrium logic and Ferrariss general logic programs to Lin and Shohams logic of knowledge and justified assumptions, a nonmonotonic modal logic that has been shown to include as special cases both Reiters default logic in the propositional case and Moores autoepistemic logic. From this mapping, we obtain a mapping from general logic programs to circumscription, both in the propositional and first-order case. Furthermore, we show that this mapping can be used to check the strong equivalence between two propositional logic programs in classical logic.